Related papers: The 3-way intersection problem for S(2, 4, v) desi…
The intersection problem for a pair of 2-(v, 3, 1) directed designs and 2-(v, 4, 1) directed designs is solved by Fu in 1983 and by Mahmoodian and Soltankhah in 1996, respectively. In this paper we determine the intersection problem for…
A $3$-$(v,\{4,6\},1)$ design is a configuration of $v$ points and a collection of $4$- and $6$-element subsets called blocks, that jointly contain every 3-element subset exactly once. Using an exhaustive computer search on $v\leq 28$ points…
The flower at a point x in a Steiner triple system (X; B) is the set of all triples containing x. Denote by J3F(r) the set of all integers k such that there exists a collection of three STS(2r+1) mutually intersecting in the same set of k +…
The intersection of two Steiner triple systems (X,A) and (X,B) is the set A intersect B. The fine intersection problem for Steiner triple systems is to determine for each v, the set I(v), consisting of all possible pairs (m,n) such that…
In this article, three types of joins are introduced for subspaces of a vector space. Decompositions of the Gra{\ss}mannian into joins are discussed. This framework admits a generalization of large set recursion methods for block designs to…
For $\mu$ given latin squares of order $n$, they have {\sf $k$ intersection} when they have $k$ identical cells and $n^2-k$ cells with mutually different entries. For each $n\geq 1$ the set of integers $k$ such that there exist $\mu$ latin…
Even though Peltesohn proved that a cyclic (v,3,1)-design exists if and only if $v\equiv 1,3\pmod{6}$ as early as 1939, the problem of determining the spectrum of cyclic (v,k,1)-designs with k>3 is far from being settled, even for k=4. This…
In this paper the fine triangle intersection problem for a pair of maximum kite packings is investigated. Let $Fin(v)={(s,t):$ $\exists$ a pair of maximum kite packings of order $v$ intersecting in $s$ blocks and $s+t$ triangles$}$. Let…
Given an STS(v), we ask if there is a permutation of the points of the design such that no $\ell$ consecutive points in this permutation contain a block of the design. Results are obtained in the cases $\ell = 3,4$.
Deciding the existence of an $l\times m\times n$ integer threeway table with given line-sums is NP-complete already for fixed $l=3$, but is in P with both $l,m$ fixed. Here we consider {\em huge} tables, where the variable dimension $n$ is…
A directed triple system of order $v$ (or, DTS$(v)$) is decomposition of the complete directed graph $\vec{K_v}$ into transitive triples. A $v$-good sequencing of a DTS$(v)$ is a permutation of the points of the design, say $[x_1 \; \cdots…
Intersection numbers for subspace designs are introduced and $q$-analogs of the Mendelsohn and K\"ohler equations are given. As an application, we are able to determine the intersection structure of a putative $q$-analog of the Fano plane…
We consider when the projective special linear group over a finite field defines a $3$-design with a cyclic starter block. We will show that the equivalences of the existence of such $3$-$(q+1,5,3)$ and $3$-$(q+1,10,18)$ designs for a prime…
Let $\mathcal D=(\Omega, \mathcal B)$ be a pair of $v$ point set $\Omega$ and a set $\mathcal B$ consists of $k$ point subsets of $\Omega$ which are called blocks. Let $d$ be the maximal cardinality of the intersections between the distinct…
It is established that up to isomorphism,there are only one (K_4-e)-design of order 6, three (K_4-e)-designs of order 10 and two (K_4-e)-designs of order 11. As an application of our enumerative results, we discuss the fine triangle…
Let S, T be surfaces in P3. Suppose that S intersect T is set-theoretically a smooth curve C of degree d and genus g. Suppose that S and T have no common singular points. Then if C is not a complete intersection, then deg(S), deg(T) < 2d^4.…
Let $v\geq6$ be an integer with $v\equiv2 \pmod 4$. In this paper, we introduce a new partitioning of the set of all $3$-subsets of a $v$-set into some simple trades.
A design is said to be $f$-pyramidal when it has an automorphism group which fixes $f$ points and acts sharply transitively on all the others. The problem of establishing the set of values of $v$ for which there exists an $f$-pyramidal…
The dimension of a block design is the maximum positive integer $d$ such that any $d$ of its points are contained in a proper subdesign. Pairwise balanced designs PBD$(v,K)$ have dimension at least two as long as not all points are on the…
In this paper, we show that for all v\pmod 1 (mod 3), there exists a super- simple (v, 4, 2) directed design. Also, we show that for these parameters there exists a super-simple (v, 4, 2) directed design whose each defining set has at least…